Information on Result #731116
Linear OA(852, 8204, F8, 13) (dual of [8204, 8152, 14]-code), using trace code based on linear OA(6426, 4102, F64, 13) (dual of [4102, 4076, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
- linear OA(6425, 4097, F64, 13) (dual of [4097, 4072, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(6421, 4097, F64, 11) (dual of [4097, 4076, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(641, 5, F64, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(853, 8205, F8, 13) (dual of [8205, 8152, 14]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(852, 8204, F8, 2, 13) (dual of [(8204, 2), 16356, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(852, 8204, F8, 3, 13) (dual of [(8204, 3), 24560, 14]-NRT-code) | [i] | ||
| 4 | Digital (39, 52, 8204)-net over F8 | [i] | ||
| 5 | Linear OA(853, 8206, F8, 13) (dual of [8206, 8153, 14]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(852, 4102, F8, 2, 13) (dual of [(4102, 2), 8152, 14]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(852, 2734, F8, 3, 13) (dual of [(2734, 3), 8150, 14]-NRT-code) | [i] | ||
| 8 | Linear OOA(852, 1367, F8, 13, 13) (dual of [(1367, 13), 17719, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |